# Deflection Angle of Light by Wormholes using the Gauss-Bonnet Theorem

## TL;DR

This paper calculates the deflection angle of light by Ellis and JNW wormholes using the Gauss-Bonnet theorem within the Gibbons-Werner method, providing a geometric approach in the weak field limit.

## Contribution

It introduces a novel application of the Gauss-Bonnet theorem to compute light deflection angles in wormhole spacetimes, expanding the geometric methods in gravitational lensing.

## Key findings

- Calculated deflection angles for Ellis and JNW wormholes
- Compared results with existing literature
- Validated the geometric approach in weak field approximation

## Abstract

In this letter, we have investigated the deflection angle of light by wormholes using a new geometrical method known as Gibbons-Werner method (GW). In particular we have calculated the deflection angle of light in the weak limit approximation in two wormhole spacetime geometries: Ellis wormhole and Janis-Newman-Winnicour (JNW) wormhole. We have employed the famous Gauss-Bonnet theorem (GBT) to the Ellis wormhole optical geometry and JNW wormhole optical geometry, respectively. By using GBT, we computed the deflection angles in leading orders by these wormholes and our results were compared with the ones in the literature.